Properties

Label 225.2.h.b.136.1
Level $225$
Weight $2$
Character 225.136
Analytic conductor $1.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.1
Root \(0.809017 + 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 225.136
Dual form 225.2.h.b.91.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.363271i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(1.80902 + 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 + 2.12663i) q^{8} +O(q^{10})\) \(q+(0.500000 - 0.363271i) q^{2} +(-0.500000 + 1.53884i) q^{4} +(1.80902 + 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 + 2.12663i) q^{8} +1.38197 q^{10} +(-0.618034 + 0.449028i) q^{11} +(3.92705 + 2.85317i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-1.50000 - 1.08981i) q^{16} +(0.236068 + 0.726543i) q^{17} +(-1.80902 - 5.56758i) q^{19} +(-2.92705 + 2.12663i) q^{20} +(-0.145898 + 0.449028i) q^{22} +(6.66312 - 4.84104i) q^{23} +(1.54508 + 4.75528i) q^{25} +3.00000 q^{26} +(0.809017 - 2.48990i) q^{28} +(0.427051 - 1.31433i) q^{29} +(-0.927051 - 2.85317i) q^{31} -5.61803 q^{32} +(0.381966 + 0.277515i) q^{34} +(-2.92705 - 2.12663i) q^{35} +(-3.42705 - 2.48990i) q^{37} +(-2.92705 - 2.12663i) q^{38} +(-1.54508 + 4.75528i) q^{40} +(-4.23607 - 3.07768i) q^{41} +1.85410 q^{43} +(-0.381966 - 1.17557i) q^{44} +(1.57295 - 4.84104i) q^{46} +(0.500000 - 1.53884i) q^{47} -4.38197 q^{49} +(2.50000 + 1.81636i) q^{50} +(-6.35410 + 4.61653i) q^{52} +(-1.69098 + 5.20431i) q^{53} -1.70820 q^{55} +(-1.11803 - 3.44095i) q^{56} +(-0.263932 - 0.812299i) q^{58} +(-3.35410 - 2.43690i) q^{59} +(3.80902 - 2.76741i) q^{61} +(-1.50000 - 1.08981i) q^{62} +(0.190983 - 0.138757i) q^{64} +(3.35410 + 10.3229i) q^{65} +(2.85410 + 8.78402i) q^{67} -1.23607 q^{68} -2.23607 q^{70} +(1.35410 - 4.16750i) q^{71} +(7.28115 - 5.29007i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(1.00000 - 0.726543i) q^{77} +(0.954915 - 2.93893i) q^{79} +(-1.28115 - 3.94298i) q^{80} -3.23607 q^{82} +(0.545085 + 1.67760i) q^{83} +(-0.527864 + 1.62460i) q^{85} +(0.927051 - 0.673542i) q^{86} +(-1.38197 - 1.00406i) q^{88} +(7.23607 - 5.25731i) q^{89} +(-6.35410 - 4.61653i) q^{91} +(4.11803 + 12.6740i) q^{92} +(-0.309017 - 0.951057i) q^{94} +(4.04508 - 12.4495i) q^{95} +(0.881966 - 2.71441i) q^{97} +(-2.19098 + 1.59184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8} + 10 q^{10} + 2 q^{11} + 9 q^{13} - q^{14} - 6 q^{16} - 8 q^{17} - 5 q^{19} - 5 q^{20} - 14 q^{22} + 11 q^{23} - 5 q^{25} + 12 q^{26} + q^{28} - 5 q^{29} + 3 q^{31} - 18 q^{32} + 6 q^{34} - 5 q^{35} - 7 q^{37} - 5 q^{38} + 5 q^{40} - 8 q^{41} - 6 q^{43} - 6 q^{44} + 13 q^{46} + 2 q^{47} - 22 q^{49} + 10 q^{50} - 12 q^{52} - 9 q^{53} + 20 q^{55} - 10 q^{58} + 13 q^{61} - 6 q^{62} + 3 q^{64} - 2 q^{67} + 4 q^{68} - 8 q^{71} + 9 q^{73} - 6 q^{74} + 20 q^{76} + 4 q^{77} + 15 q^{79} + 15 q^{80} - 4 q^{82} - 9 q^{83} - 20 q^{85} - 3 q^{86} - 10 q^{88} + 20 q^{89} - 12 q^{91} + 12 q^{92} + q^{94} + 5 q^{95} + 8 q^{97} - 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.363271i 0.353553 0.256872i −0.396805 0.917903i \(-0.629881\pi\)
0.750358 + 0.661031i \(0.229881\pi\)
\(3\) 0 0
\(4\) −0.500000 + 1.53884i −0.250000 + 0.769421i
\(5\) 1.80902 + 1.31433i 0.809017 + 0.587785i
\(6\) 0 0
\(7\) −1.61803 −0.611559 −0.305780 0.952102i \(-0.598917\pi\)
−0.305780 + 0.952102i \(0.598917\pi\)
\(8\) 0.690983 + 2.12663i 0.244299 + 0.751876i
\(9\) 0 0
\(10\) 1.38197 0.437016
\(11\) −0.618034 + 0.449028i −0.186344 + 0.135387i −0.677046 0.735940i \(-0.736740\pi\)
0.490702 + 0.871327i \(0.336740\pi\)
\(12\) 0 0
\(13\) 3.92705 + 2.85317i 1.08917 + 0.791327i 0.979259 0.202615i \(-0.0649439\pi\)
0.109909 + 0.993942i \(0.464944\pi\)
\(14\) −0.809017 + 0.587785i −0.216219 + 0.157092i
\(15\) 0 0
\(16\) −1.50000 1.08981i −0.375000 0.272453i
\(17\) 0.236068 + 0.726543i 0.0572549 + 0.176212i 0.975594 0.219582i \(-0.0704693\pi\)
−0.918339 + 0.395794i \(0.870469\pi\)
\(18\) 0 0
\(19\) −1.80902 5.56758i −0.415017 1.27729i −0.912236 0.409666i \(-0.865645\pi\)
0.497219 0.867625i \(-0.334355\pi\)
\(20\) −2.92705 + 2.12663i −0.654508 + 0.475528i
\(21\) 0 0
\(22\) −0.145898 + 0.449028i −0.0311056 + 0.0957331i
\(23\) 6.66312 4.84104i 1.38936 1.00943i 0.393421 0.919359i \(-0.371292\pi\)
0.995936 0.0900679i \(-0.0287084\pi\)
\(24\) 0 0
\(25\) 1.54508 + 4.75528i 0.309017 + 0.951057i
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) 0.809017 2.48990i 0.152890 0.470547i
\(29\) 0.427051 1.31433i 0.0793014 0.244065i −0.903544 0.428495i \(-0.859044\pi\)
0.982846 + 0.184430i \(0.0590440\pi\)
\(30\) 0 0
\(31\) −0.927051 2.85317i −0.166503 0.512444i 0.832641 0.553814i \(-0.186828\pi\)
−0.999144 + 0.0413693i \(0.986828\pi\)
\(32\) −5.61803 −0.993137
\(33\) 0 0
\(34\) 0.381966 + 0.277515i 0.0655066 + 0.0475934i
\(35\) −2.92705 2.12663i −0.494762 0.359466i
\(36\) 0 0
\(37\) −3.42705 2.48990i −0.563404 0.409337i 0.269299 0.963057i \(-0.413208\pi\)
−0.832703 + 0.553720i \(0.813208\pi\)
\(38\) −2.92705 2.12663i −0.474830 0.344984i
\(39\) 0 0
\(40\) −1.54508 + 4.75528i −0.244299 + 0.751876i
\(41\) −4.23607 3.07768i −0.661563 0.480653i 0.205628 0.978630i \(-0.434076\pi\)
−0.867190 + 0.497977i \(0.834076\pi\)
\(42\) 0 0
\(43\) 1.85410 0.282748 0.141374 0.989956i \(-0.454848\pi\)
0.141374 + 0.989956i \(0.454848\pi\)
\(44\) −0.381966 1.17557i −0.0575835 0.177224i
\(45\) 0 0
\(46\) 1.57295 4.84104i 0.231919 0.713772i
\(47\) 0.500000 1.53884i 0.0729325 0.224463i −0.907945 0.419089i \(-0.862349\pi\)
0.980877 + 0.194626i \(0.0623494\pi\)
\(48\) 0 0
\(49\) −4.38197 −0.625995
\(50\) 2.50000 + 1.81636i 0.353553 + 0.256872i
\(51\) 0 0
\(52\) −6.35410 + 4.61653i −0.881155 + 0.640197i
\(53\) −1.69098 + 5.20431i −0.232274 + 0.714867i 0.765197 + 0.643796i \(0.222642\pi\)
−0.997471 + 0.0710707i \(0.977358\pi\)
\(54\) 0 0
\(55\) −1.70820 −0.230334
\(56\) −1.11803 3.44095i −0.149404 0.459817i
\(57\) 0 0
\(58\) −0.263932 0.812299i −0.0346560 0.106660i
\(59\) −3.35410 2.43690i −0.436667 0.317257i 0.347642 0.937627i \(-0.386982\pi\)
−0.784309 + 0.620370i \(0.786982\pi\)
\(60\) 0 0
\(61\) 3.80902 2.76741i 0.487695 0.354331i −0.316602 0.948558i \(-0.602542\pi\)
0.804297 + 0.594227i \(0.202542\pi\)
\(62\) −1.50000 1.08981i −0.190500 0.138406i
\(63\) 0 0
\(64\) 0.190983 0.138757i 0.0238729 0.0173447i
\(65\) 3.35410 + 10.3229i 0.416025 + 1.28039i
\(66\) 0 0
\(67\) 2.85410 + 8.78402i 0.348684 + 1.07314i 0.959582 + 0.281430i \(0.0908086\pi\)
−0.610898 + 0.791709i \(0.709191\pi\)
\(68\) −1.23607 −0.149895
\(69\) 0 0
\(70\) −2.23607 −0.267261
\(71\) 1.35410 4.16750i 0.160702 0.494591i −0.837992 0.545683i \(-0.816270\pi\)
0.998694 + 0.0510922i \(0.0162702\pi\)
\(72\) 0 0
\(73\) 7.28115 5.29007i 0.852194 0.619156i −0.0735557 0.997291i \(-0.523435\pi\)
0.925750 + 0.378136i \(0.123435\pi\)
\(74\) −2.61803 −0.304340
\(75\) 0 0
\(76\) 9.47214 1.08653
\(77\) 1.00000 0.726543i 0.113961 0.0827972i
\(78\) 0 0
\(79\) 0.954915 2.93893i 0.107436 0.330655i −0.882858 0.469640i \(-0.844384\pi\)
0.990295 + 0.138985i \(0.0443839\pi\)
\(80\) −1.28115 3.94298i −0.143237 0.440839i
\(81\) 0 0
\(82\) −3.23607 −0.357364
\(83\) 0.545085 + 1.67760i 0.0598308 + 0.184140i 0.976505 0.215495i \(-0.0691366\pi\)
−0.916674 + 0.399636i \(0.869137\pi\)
\(84\) 0 0
\(85\) −0.527864 + 1.62460i −0.0572549 + 0.176212i
\(86\) 0.927051 0.673542i 0.0999665 0.0726299i
\(87\) 0 0
\(88\) −1.38197 1.00406i −0.147318 0.107033i
\(89\) 7.23607 5.25731i 0.767022 0.557274i −0.134034 0.990977i \(-0.542793\pi\)
0.901056 + 0.433703i \(0.142793\pi\)
\(90\) 0 0
\(91\) −6.35410 4.61653i −0.666091 0.483943i
\(92\) 4.11803 + 12.6740i 0.429335 + 1.32136i
\(93\) 0 0
\(94\) −0.309017 0.951057i −0.0318727 0.0980940i
\(95\) 4.04508 12.4495i 0.415017 1.27729i
\(96\) 0 0
\(97\) 0.881966 2.71441i 0.0895501 0.275607i −0.896245 0.443559i \(-0.853716\pi\)
0.985795 + 0.167953i \(0.0537155\pi\)
\(98\) −2.19098 + 1.59184i −0.221323 + 0.160800i
\(99\) 0 0
\(100\) −8.09017 −0.809017
\(101\) 7.47214 0.743505 0.371753 0.928332i \(-0.378757\pi\)
0.371753 + 0.928332i \(0.378757\pi\)
\(102\) 0 0
\(103\) −3.57295 + 10.9964i −0.352053 + 1.08351i 0.605645 + 0.795735i \(0.292915\pi\)
−0.957699 + 0.287773i \(0.907085\pi\)
\(104\) −3.35410 + 10.3229i −0.328897 + 1.01224i
\(105\) 0 0
\(106\) 1.04508 + 3.21644i 0.101508 + 0.312408i
\(107\) −10.4164 −1.00699 −0.503496 0.863998i \(-0.667953\pi\)
−0.503496 + 0.863998i \(0.667953\pi\)
\(108\) 0 0
\(109\) −8.09017 5.87785i −0.774898 0.562996i 0.128546 0.991704i \(-0.458969\pi\)
−0.903443 + 0.428707i \(0.858969\pi\)
\(110\) −0.854102 + 0.620541i −0.0814354 + 0.0591663i
\(111\) 0 0
\(112\) 2.42705 + 1.76336i 0.229335 + 0.166621i
\(113\) 8.20820 + 5.96361i 0.772163 + 0.561009i 0.902617 0.430445i \(-0.141643\pi\)
−0.130454 + 0.991454i \(0.541643\pi\)
\(114\) 0 0
\(115\) 18.4164 1.71734
\(116\) 1.80902 + 1.31433i 0.167963 + 0.122032i
\(117\) 0 0
\(118\) −2.56231 −0.235879
\(119\) −0.381966 1.17557i −0.0350148 0.107764i
\(120\) 0 0
\(121\) −3.21885 + 9.90659i −0.292622 + 0.900599i
\(122\) 0.899187 2.76741i 0.0814086 0.250550i
\(123\) 0 0
\(124\) 4.85410 0.435911
\(125\) −3.45492 + 10.6331i −0.309017 + 0.951057i
\(126\) 0 0
\(127\) 12.8541 9.33905i 1.14062 0.828707i 0.153412 0.988162i \(-0.450974\pi\)
0.987205 + 0.159455i \(0.0509738\pi\)
\(128\) 3.51722 10.8249i 0.310881 0.956794i
\(129\) 0 0
\(130\) 5.42705 + 3.94298i 0.475984 + 0.345823i
\(131\) 5.50000 + 16.9273i 0.480537 + 1.47894i 0.838342 + 0.545145i \(0.183525\pi\)
−0.357805 + 0.933797i \(0.616475\pi\)
\(132\) 0 0
\(133\) 2.92705 + 9.00854i 0.253808 + 0.781139i
\(134\) 4.61803 + 3.35520i 0.398937 + 0.289845i
\(135\) 0 0
\(136\) −1.38197 + 1.00406i −0.118503 + 0.0860972i
\(137\) 4.80902 + 3.49396i 0.410862 + 0.298509i 0.773951 0.633246i \(-0.218278\pi\)
−0.363089 + 0.931755i \(0.618278\pi\)
\(138\) 0 0
\(139\) −4.04508 + 2.93893i −0.343100 + 0.249276i −0.745968 0.665981i \(-0.768013\pi\)
0.402869 + 0.915258i \(0.368013\pi\)
\(140\) 4.73607 3.44095i 0.400271 0.290814i
\(141\) 0 0
\(142\) −0.836881 2.57565i −0.0702295 0.216144i
\(143\) −3.70820 −0.310096
\(144\) 0 0
\(145\) 2.50000 1.81636i 0.207614 0.150840i
\(146\) 1.71885 5.29007i 0.142253 0.437809i
\(147\) 0 0
\(148\) 5.54508 4.02874i 0.455803 0.331160i
\(149\) −13.9443 −1.14236 −0.571180 0.820825i \(-0.693514\pi\)
−0.571180 + 0.820825i \(0.693514\pi\)
\(150\) 0 0
\(151\) −5.56231 −0.452654 −0.226327 0.974051i \(-0.572672\pi\)
−0.226327 + 0.974051i \(0.572672\pi\)
\(152\) 10.5902 7.69421i 0.858976 0.624083i
\(153\) 0 0
\(154\) 0.236068 0.726543i 0.0190229 0.0585465i
\(155\) 2.07295 6.37988i 0.166503 0.512444i
\(156\) 0 0
\(157\) −9.18034 −0.732671 −0.366335 0.930483i \(-0.619388\pi\)
−0.366335 + 0.930483i \(0.619388\pi\)
\(158\) −0.590170 1.81636i −0.0469514 0.144502i
\(159\) 0 0
\(160\) −10.1631 7.38394i −0.803465 0.583752i
\(161\) −10.7812 + 7.83297i −0.849674 + 0.617324i
\(162\) 0 0
\(163\) −8.89919 6.46564i −0.697038 0.506428i 0.181928 0.983312i \(-0.441766\pi\)
−0.878966 + 0.476884i \(0.841766\pi\)
\(164\) 6.85410 4.97980i 0.535215 0.388857i
\(165\) 0 0
\(166\) 0.881966 + 0.640786i 0.0684538 + 0.0497346i
\(167\) 1.71885 + 5.29007i 0.133008 + 0.409358i 0.995275 0.0970971i \(-0.0309557\pi\)
−0.862267 + 0.506455i \(0.830956\pi\)
\(168\) 0 0
\(169\) 3.26393 + 10.0453i 0.251072 + 0.772719i
\(170\) 0.326238 + 1.00406i 0.0250213 + 0.0770077i
\(171\) 0 0
\(172\) −0.927051 + 2.85317i −0.0706870 + 0.217552i
\(173\) −13.6631 + 9.92684i −1.03879 + 0.754723i −0.970049 0.242911i \(-0.921898\pi\)
−0.0687392 + 0.997635i \(0.521898\pi\)
\(174\) 0 0
\(175\) −2.50000 7.69421i −0.188982 0.581628i
\(176\) 1.41641 0.106766
\(177\) 0 0
\(178\) 1.70820 5.25731i 0.128035 0.394052i
\(179\) 2.92705 9.00854i 0.218778 0.673330i −0.780086 0.625673i \(-0.784825\pi\)
0.998864 0.0476570i \(-0.0151754\pi\)
\(180\) 0 0
\(181\) 4.23607 + 13.0373i 0.314864 + 0.969053i 0.975810 + 0.218619i \(0.0701553\pi\)
−0.660946 + 0.750434i \(0.729845\pi\)
\(182\) −4.85410 −0.359810
\(183\) 0 0
\(184\) 14.8992 + 10.8249i 1.09838 + 0.798022i
\(185\) −2.92705 9.00854i −0.215201 0.662321i
\(186\) 0 0
\(187\) −0.472136 0.343027i −0.0345260 0.0250846i
\(188\) 2.11803 + 1.53884i 0.154474 + 0.112232i
\(189\) 0 0
\(190\) −2.50000 7.69421i −0.181369 0.558197i
\(191\) −19.5623 14.2128i −1.41548 1.02841i −0.992497 0.122267i \(-0.960984\pi\)
−0.422982 0.906138i \(-0.639016\pi\)
\(192\) 0 0
\(193\) −5.70820 −0.410886 −0.205443 0.978669i \(-0.565863\pi\)
−0.205443 + 0.978669i \(0.565863\pi\)
\(194\) −0.545085 1.67760i −0.0391348 0.120445i
\(195\) 0 0
\(196\) 2.19098 6.74315i 0.156499 0.481654i
\(197\) 3.00000 9.23305i 0.213741 0.657828i −0.785499 0.618862i \(-0.787594\pi\)
0.999241 0.0389652i \(-0.0124062\pi\)
\(198\) 0 0
\(199\) 2.56231 0.181637 0.0908185 0.995867i \(-0.471052\pi\)
0.0908185 + 0.995867i \(0.471052\pi\)
\(200\) −9.04508 + 6.57164i −0.639584 + 0.464685i
\(201\) 0 0
\(202\) 3.73607 2.71441i 0.262869 0.190985i
\(203\) −0.690983 + 2.12663i −0.0484975 + 0.149260i
\(204\) 0 0
\(205\) −3.61803 11.1352i −0.252694 0.777714i
\(206\) 2.20820 + 6.79615i 0.153853 + 0.473510i
\(207\) 0 0
\(208\) −2.78115 8.55951i −0.192838 0.593495i
\(209\) 3.61803 + 2.62866i 0.250265 + 0.181828i
\(210\) 0 0
\(211\) −10.6631 + 7.74721i −0.734079 + 0.533340i −0.890851 0.454295i \(-0.849891\pi\)
0.156772 + 0.987635i \(0.449891\pi\)
\(212\) −7.16312 5.20431i −0.491965 0.357434i
\(213\) 0 0
\(214\) −5.20820 + 3.78398i −0.356025 + 0.258668i
\(215\) 3.35410 + 2.43690i 0.228748 + 0.166195i
\(216\) 0 0
\(217\) 1.50000 + 4.61653i 0.101827 + 0.313390i
\(218\) −6.18034 −0.418585
\(219\) 0 0
\(220\) 0.854102 2.62866i 0.0575835 0.177224i
\(221\) −1.14590 + 3.52671i −0.0770814 + 0.237232i
\(222\) 0 0
\(223\) −17.9443 + 13.0373i −1.20164 + 0.873041i −0.994445 0.105260i \(-0.966433\pi\)
−0.207193 + 0.978300i \(0.566433\pi\)
\(224\) 9.09017 0.607363
\(225\) 0 0
\(226\) 6.27051 0.417108
\(227\) 15.5623 11.3067i 1.03291 0.750451i 0.0640182 0.997949i \(-0.479608\pi\)
0.968888 + 0.247498i \(0.0796084\pi\)
\(228\) 0 0
\(229\) 2.56231 7.88597i 0.169322 0.521119i −0.830007 0.557753i \(-0.811664\pi\)
0.999329 + 0.0366339i \(0.0116635\pi\)
\(230\) 9.20820 6.69015i 0.607171 0.441136i
\(231\) 0 0
\(232\) 3.09017 0.202880
\(233\) −4.61803 14.2128i −0.302537 0.931115i −0.980585 0.196096i \(-0.937174\pi\)
0.678047 0.735018i \(-0.262826\pi\)
\(234\) 0 0
\(235\) 2.92705 2.12663i 0.190940 0.138726i
\(236\) 5.42705 3.94298i 0.353271 0.256666i
\(237\) 0 0
\(238\) −0.618034 0.449028i −0.0400612 0.0291062i
\(239\) −23.8435 + 17.3233i −1.54231 + 1.12055i −0.593436 + 0.804881i \(0.702229\pi\)
−0.948869 + 0.315669i \(0.897771\pi\)
\(240\) 0 0
\(241\) −9.28115 6.74315i −0.597852 0.434365i 0.247264 0.968948i \(-0.420468\pi\)
−0.845116 + 0.534584i \(0.820468\pi\)
\(242\) 1.98936 + 6.12261i 0.127881 + 0.393576i
\(243\) 0 0
\(244\) 2.35410 + 7.24518i 0.150706 + 0.463825i
\(245\) −7.92705 5.75934i −0.506441 0.367951i
\(246\) 0 0
\(247\) 8.78115 27.0256i 0.558731 1.71960i
\(248\) 5.42705 3.94298i 0.344618 0.250380i
\(249\) 0 0
\(250\) 2.13525 + 6.57164i 0.135045 + 0.415627i
\(251\) 6.81966 0.430453 0.215227 0.976564i \(-0.430951\pi\)
0.215227 + 0.976564i \(0.430951\pi\)
\(252\) 0 0
\(253\) −1.94427 + 5.98385i −0.122235 + 0.376202i
\(254\) 3.03444 9.33905i 0.190398 0.585984i
\(255\) 0 0
\(256\) −2.02786 6.24112i −0.126742 0.390070i
\(257\) −16.1459 −1.00715 −0.503577 0.863951i \(-0.667983\pi\)
−0.503577 + 0.863951i \(0.667983\pi\)
\(258\) 0 0
\(259\) 5.54508 + 4.02874i 0.344555 + 0.250334i
\(260\) −17.5623 −1.08917
\(261\) 0 0
\(262\) 8.89919 + 6.46564i 0.549794 + 0.399448i
\(263\) −17.8713 12.9843i −1.10199 0.800645i −0.120609 0.992700i \(-0.538485\pi\)
−0.981384 + 0.192055i \(0.938485\pi\)
\(264\) 0 0
\(265\) −9.89919 + 7.19218i −0.608102 + 0.441812i
\(266\) 4.73607 + 3.44095i 0.290387 + 0.210978i
\(267\) 0 0
\(268\) −14.9443 −0.912867
\(269\) 5.32624 + 16.3925i 0.324746 + 0.999467i 0.971555 + 0.236814i \(0.0761033\pi\)
−0.646808 + 0.762652i \(0.723897\pi\)
\(270\) 0 0
\(271\) −2.47214 + 7.60845i −0.150172 + 0.462181i −0.997640 0.0686657i \(-0.978126\pi\)
0.847468 + 0.530846i \(0.178126\pi\)
\(272\) 0.437694 1.34708i 0.0265391 0.0816790i
\(273\) 0 0
\(274\) 3.67376 0.221940
\(275\) −3.09017 2.24514i −0.186344 0.135387i
\(276\) 0 0
\(277\) 9.13525 6.63715i 0.548884 0.398788i −0.278490 0.960439i \(-0.589834\pi\)
0.827374 + 0.561651i \(0.189834\pi\)
\(278\) −0.954915 + 2.93893i −0.0572720 + 0.176265i
\(279\) 0 0
\(280\) 2.50000 7.69421i 0.149404 0.459817i
\(281\) 0.336881 + 1.03681i 0.0200966 + 0.0618511i 0.960602 0.277928i \(-0.0896477\pi\)
−0.940505 + 0.339779i \(0.889648\pi\)
\(282\) 0 0
\(283\) −7.15248 22.0131i −0.425171 1.30854i −0.902831 0.429996i \(-0.858515\pi\)
0.477660 0.878545i \(-0.341485\pi\)
\(284\) 5.73607 + 4.16750i 0.340373 + 0.247295i
\(285\) 0 0
\(286\) −1.85410 + 1.34708i −0.109635 + 0.0796547i
\(287\) 6.85410 + 4.97980i 0.404585 + 0.293948i
\(288\) 0 0
\(289\) 13.2812 9.64932i 0.781244 0.567607i
\(290\) 0.590170 1.81636i 0.0346560 0.106660i
\(291\) 0 0
\(292\) 4.50000 + 13.8496i 0.263343 + 0.810485i
\(293\) 28.4721 1.66336 0.831680 0.555255i \(-0.187379\pi\)
0.831680 + 0.555255i \(0.187379\pi\)
\(294\) 0 0
\(295\) −2.86475 8.81678i −0.166792 0.513333i
\(296\) 2.92705 9.00854i 0.170131 0.523611i
\(297\) 0 0
\(298\) −6.97214 + 5.06555i −0.403885 + 0.293440i
\(299\) 39.9787 2.31203
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) −2.78115 + 2.02063i −0.160037 + 0.116274i
\(303\) 0 0
\(304\) −3.35410 + 10.3229i −0.192371 + 0.592057i
\(305\) 10.5279 0.602824
\(306\) 0 0
\(307\) 4.76393 0.271892 0.135946 0.990716i \(-0.456593\pi\)
0.135946 + 0.990716i \(0.456593\pi\)
\(308\) 0.618034 + 1.90211i 0.0352158 + 0.108383i
\(309\) 0 0
\(310\) −1.28115 3.94298i −0.0727646 0.223946i
\(311\) −23.8713 + 17.3435i −1.35362 + 0.983461i −0.354796 + 0.934944i \(0.615450\pi\)
−0.998822 + 0.0485178i \(0.984550\pi\)
\(312\) 0 0
\(313\) 17.1803 + 12.4822i 0.971090 + 0.705538i 0.955700 0.294343i \(-0.0951009\pi\)
0.0153904 + 0.999882i \(0.495101\pi\)
\(314\) −4.59017 + 3.33495i −0.259038 + 0.188202i
\(315\) 0 0
\(316\) 4.04508 + 2.93893i 0.227554 + 0.165328i
\(317\) 7.30902 + 22.4948i 0.410515 + 1.26344i 0.916201 + 0.400719i \(0.131239\pi\)
−0.505686 + 0.862718i \(0.668761\pi\)
\(318\) 0 0
\(319\) 0.326238 + 1.00406i 0.0182658 + 0.0562164i
\(320\) 0.527864 0.0295085
\(321\) 0 0
\(322\) −2.54508 + 7.83297i −0.141832 + 0.436514i
\(323\) 3.61803 2.62866i 0.201313 0.146262i
\(324\) 0 0
\(325\) −7.50000 + 23.0826i −0.416025 + 1.28039i
\(326\) −6.79837 −0.376527
\(327\) 0 0
\(328\) 3.61803 11.1352i 0.199773 0.614837i
\(329\) −0.809017 + 2.48990i −0.0446026 + 0.137273i
\(330\) 0 0
\(331\) 5.29180 + 16.2865i 0.290863 + 0.895186i 0.984580 + 0.174937i \(0.0559722\pi\)
−0.693716 + 0.720248i \(0.744028\pi\)
\(332\) −2.85410 −0.156639
\(333\) 0 0
\(334\) 2.78115 + 2.02063i 0.152178 + 0.110564i
\(335\) −6.38197 + 19.6417i −0.348684 + 1.07314i
\(336\) 0 0
\(337\) −0.927051 0.673542i −0.0504997 0.0366902i 0.562249 0.826968i \(-0.309936\pi\)
−0.612749 + 0.790278i \(0.709936\pi\)
\(338\) 5.28115 + 3.83698i 0.287257 + 0.208704i
\(339\) 0 0
\(340\) −2.23607 1.62460i −0.121268 0.0881062i
\(341\) 1.85410 + 1.34708i 0.100405 + 0.0729487i
\(342\) 0 0
\(343\) 18.4164 0.994393
\(344\) 1.28115 + 3.94298i 0.0690751 + 0.212591i
\(345\) 0 0
\(346\) −3.22542 + 9.92684i −0.173400 + 0.533670i
\(347\) 9.60739 29.5685i 0.515752 1.58732i −0.266158 0.963929i \(-0.585754\pi\)
0.781910 0.623391i \(-0.214246\pi\)
\(348\) 0 0
\(349\) 8.29180 0.443850 0.221925 0.975064i \(-0.428766\pi\)
0.221925 + 0.975064i \(0.428766\pi\)
\(350\) −4.04508 2.93893i −0.216219 0.157092i
\(351\) 0 0
\(352\) 3.47214 2.52265i 0.185065 0.134458i
\(353\) −7.44427 + 22.9111i −0.396219 + 1.21944i 0.531790 + 0.846876i \(0.321520\pi\)
−0.928008 + 0.372559i \(0.878480\pi\)
\(354\) 0 0
\(355\) 7.92705 5.75934i 0.420724 0.305674i
\(356\) 4.47214 + 13.7638i 0.237023 + 0.729481i
\(357\) 0 0
\(358\) −1.80902 5.56758i −0.0956095 0.294256i
\(359\) −23.2533 16.8945i −1.22726 0.891658i −0.230580 0.973053i \(-0.574062\pi\)
−0.996682 + 0.0813956i \(0.974062\pi\)
\(360\) 0 0
\(361\) −12.3541 + 8.97578i −0.650216 + 0.472409i
\(362\) 6.85410 + 4.97980i 0.360244 + 0.261732i
\(363\) 0 0
\(364\) 10.2812 7.46969i 0.538879 0.391518i
\(365\) 20.1246 1.05337
\(366\) 0 0
\(367\) −1.68034 5.17155i −0.0877130 0.269953i 0.897573 0.440866i \(-0.145328\pi\)
−0.985286 + 0.170913i \(0.945328\pi\)
\(368\) −15.2705 −0.796030
\(369\) 0 0
\(370\) −4.73607 3.44095i −0.246216 0.178887i
\(371\) 2.73607 8.42075i 0.142050 0.437184i
\(372\) 0 0
\(373\) −4.26393 + 3.09793i −0.220778 + 0.160405i −0.692677 0.721248i \(-0.743569\pi\)
0.471899 + 0.881653i \(0.343569\pi\)
\(374\) −0.360680 −0.0186503
\(375\) 0 0
\(376\) 3.61803 0.186586
\(377\) 5.42705 3.94298i 0.279507 0.203074i
\(378\) 0 0
\(379\) −10.6910 + 32.9035i −0.549159 + 1.69014i 0.161732 + 0.986835i \(0.448292\pi\)
−0.710891 + 0.703303i \(0.751708\pi\)
\(380\) 17.1353 + 12.4495i 0.879020 + 0.638645i
\(381\) 0 0
\(382\) −14.9443 −0.764615
\(383\) 3.51064 + 10.8046i 0.179385 + 0.552092i 0.999807 0.0196680i \(-0.00626093\pi\)
−0.820421 + 0.571760i \(0.806261\pi\)
\(384\) 0 0
\(385\) 2.76393 0.140863
\(386\) −2.85410 + 2.07363i −0.145270 + 0.105545i
\(387\) 0 0
\(388\) 3.73607 + 2.71441i 0.189670 + 0.137803i
\(389\) 12.1353 8.81678i 0.615282 0.447028i −0.235988 0.971756i \(-0.575833\pi\)
0.851270 + 0.524727i \(0.175833\pi\)
\(390\) 0 0
\(391\) 5.09017 + 3.69822i 0.257421 + 0.187027i
\(392\) −3.02786 9.31881i −0.152930 0.470671i
\(393\) 0 0
\(394\) −1.85410 5.70634i −0.0934083 0.287481i
\(395\) 5.59017 4.06150i 0.281272 0.204356i
\(396\) 0 0
\(397\) −0.0106431 + 0.0327561i −0.000534163 + 0.00164398i −0.951323 0.308195i \(-0.900275\pi\)
0.950789 + 0.309839i \(0.100275\pi\)
\(398\) 1.28115 0.930812i 0.0642184 0.0466574i
\(399\) 0 0
\(400\) 2.86475 8.81678i 0.143237 0.440839i
\(401\) 22.5967 1.12843 0.564214 0.825629i \(-0.309179\pi\)
0.564214 + 0.825629i \(0.309179\pi\)
\(402\) 0 0
\(403\) 4.50000 13.8496i 0.224161 0.689897i
\(404\) −3.73607 + 11.4984i −0.185876 + 0.572069i
\(405\) 0 0
\(406\) 0.427051 + 1.31433i 0.0211942 + 0.0652290i
\(407\) 3.23607 0.160406
\(408\) 0 0
\(409\) −22.9894 16.7027i −1.13675 0.825898i −0.150087 0.988673i \(-0.547955\pi\)
−0.986663 + 0.162775i \(0.947955\pi\)
\(410\) −5.85410 4.25325i −0.289113 0.210053i
\(411\) 0 0
\(412\) −15.1353 10.9964i −0.745660 0.541754i
\(413\) 5.42705 + 3.94298i 0.267048 + 0.194022i
\(414\) 0 0
\(415\) −1.21885 + 3.75123i −0.0598308 + 0.184140i
\(416\) −22.0623 16.0292i −1.08169 0.785896i
\(417\) 0 0
\(418\) 2.76393 0.135188
\(419\) 0.163119 + 0.502029i 0.00796888 + 0.0245257i 0.954962 0.296728i \(-0.0958956\pi\)
−0.946993 + 0.321254i \(0.895896\pi\)
\(420\) 0 0
\(421\) 9.88854 30.4338i 0.481938 1.48325i −0.354429 0.935083i \(-0.615325\pi\)
0.836367 0.548170i \(-0.184675\pi\)
\(422\) −2.51722 + 7.74721i −0.122536 + 0.377128i
\(423\) 0 0
\(424\) −12.2361 −0.594236
\(425\) −3.09017 + 2.24514i −0.149895 + 0.108905i
\(426\) 0 0
\(427\) −6.16312 + 4.47777i −0.298254 + 0.216694i
\(428\) 5.20820 16.0292i 0.251748 0.774801i
\(429\) 0 0
\(430\) 2.56231 0.123565
\(431\) −7.36475 22.6664i −0.354747 1.09180i −0.956156 0.292858i \(-0.905394\pi\)
0.601409 0.798942i \(-0.294606\pi\)
\(432\) 0 0
\(433\) 6.22542 + 19.1599i 0.299175 + 0.920765i 0.981787 + 0.189985i \(0.0608438\pi\)
−0.682612 + 0.730781i \(0.739156\pi\)
\(434\) 2.42705 + 1.76336i 0.116502 + 0.0846438i
\(435\) 0 0
\(436\) 13.0902 9.51057i 0.626905 0.455473i
\(437\) −39.0066 28.3399i −1.86594 1.35568i
\(438\) 0 0
\(439\) −4.83688 + 3.51420i −0.230852 + 0.167724i −0.697198 0.716879i \(-0.745570\pi\)
0.466346 + 0.884602i \(0.345570\pi\)
\(440\) −1.18034 3.63271i −0.0562705 0.173183i
\(441\) 0 0
\(442\) 0.708204 + 2.17963i 0.0336858 + 0.103674i
\(443\) −12.0557 −0.572785 −0.286392 0.958112i \(-0.592456\pi\)
−0.286392 + 0.958112i \(0.592456\pi\)
\(444\) 0 0
\(445\) 20.0000 0.948091
\(446\) −4.23607 + 13.0373i −0.200584 + 0.617333i
\(447\) 0 0
\(448\) −0.309017 + 0.224514i −0.0145997 + 0.0106073i
\(449\) −20.3262 −0.959254 −0.479627 0.877472i \(-0.659228\pi\)
−0.479627 + 0.877472i \(0.659228\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) −13.2812 + 9.64932i −0.624693 + 0.453866i
\(453\) 0 0
\(454\) 3.67376 11.3067i 0.172418 0.530649i
\(455\) −5.42705 16.7027i −0.254424 0.783037i
\(456\) 0 0
\(457\) 5.41641 0.253369 0.126684 0.991943i \(-0.459566\pi\)
0.126684 + 0.991943i \(0.459566\pi\)
\(458\) −1.58359 4.87380i −0.0739964 0.227738i
\(459\) 0 0
\(460\) −9.20820 + 28.3399i −0.429335 + 1.32136i
\(461\) 18.7533 13.6251i 0.873428 0.634582i −0.0580768 0.998312i \(-0.518497\pi\)
0.931505 + 0.363730i \(0.118497\pi\)
\(462\) 0 0
\(463\) −13.0451 9.47781i −0.606257 0.440471i 0.241838 0.970317i \(-0.422250\pi\)
−0.848094 + 0.529846i \(0.822250\pi\)
\(464\) −2.07295 + 1.50609i −0.0962342 + 0.0699183i
\(465\) 0 0
\(466\) −7.47214 5.42882i −0.346140 0.251485i
\(467\) 8.79180 + 27.0584i 0.406836 + 1.25211i 0.919353 + 0.393435i \(0.128713\pi\)
−0.512517 + 0.858677i \(0.671287\pi\)
\(468\) 0 0
\(469\) −4.61803 14.2128i −0.213241 0.656288i
\(470\) 0.690983 2.12663i 0.0318727 0.0980940i
\(471\) 0 0
\(472\) 2.86475 8.81678i 0.131861 0.405825i
\(473\) −1.14590 + 0.832544i −0.0526884 + 0.0382804i
\(474\) 0 0
\(475\) 23.6803 17.2048i 1.08653 0.789409i
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) −5.62868 + 17.3233i −0.257450 + 0.792349i
\(479\) 1.28115 3.94298i 0.0585374 0.180160i −0.917512 0.397708i \(-0.869806\pi\)
0.976050 + 0.217548i \(0.0698059\pi\)
\(480\) 0 0
\(481\) −6.35410 19.5559i −0.289722 0.891673i
\(482\) −7.09017 −0.322948
\(483\) 0 0
\(484\) −13.6353 9.90659i −0.619784 0.450300i
\(485\) 5.16312 3.75123i 0.234445 0.170334i
\(486\) 0 0
\(487\) 7.75329 + 5.63309i 0.351335 + 0.255260i 0.749429 0.662085i \(-0.230328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(488\) 8.51722 + 6.18812i 0.385556 + 0.280123i
\(489\) 0 0
\(490\) −6.05573 −0.273570
\(491\) 30.1353 + 21.8945i 1.35999 + 0.988087i 0.998446 + 0.0557300i \(0.0177486\pi\)
0.361539 + 0.932357i \(0.382251\pi\)
\(492\) 0 0
\(493\) 1.05573 0.0475476
\(494\) −5.42705 16.7027i −0.244175 0.751492i
\(495\) 0 0
\(496\) −1.71885 + 5.29007i −0.0771785 + 0.237531i
\(497\) −2.19098 + 6.74315i −0.0982790 + 0.302472i
\(498\) 0 0
\(499\) −12.5623 −0.562366 −0.281183 0.959654i \(-0.590727\pi\)
−0.281183 + 0.959654i \(0.590727\pi\)
\(500\) −14.6353 10.6331i −0.654508 0.475528i
\(501\) 0 0
\(502\) 3.40983 2.47739i 0.152188 0.110571i
\(503\) 3.27051 10.0656i 0.145825 0.448803i −0.851291 0.524693i \(-0.824180\pi\)
0.997116 + 0.0758907i \(0.0241800\pi\)
\(504\) 0 0
\(505\) 13.5172 + 9.82084i 0.601508 + 0.437021i
\(506\) 1.20163 + 3.69822i 0.0534188 + 0.164406i
\(507\) 0 0
\(508\) 7.94427 + 24.4500i 0.352470 + 1.08479i
\(509\) −3.78115 2.74717i −0.167597 0.121766i 0.500825 0.865548i \(-0.333030\pi\)
−0.668422 + 0.743782i \(0.733030\pi\)
\(510\) 0 0
\(511\) −11.7812 + 8.55951i −0.521168 + 0.378650i
\(512\) 15.1353 + 10.9964i 0.668890 + 0.485977i
\(513\) 0 0
\(514\) −8.07295 + 5.86534i −0.356083 + 0.258709i
\(515\) −20.9164 + 15.1967i −0.921687 + 0.669645i
\(516\) 0 0
\(517\) 0.381966 + 1.17557i 0.0167988 + 0.0517015i
\(518\) 4.23607 0.186122
\(519\) 0 0
\(520\) −19.6353 + 14.2658i −0.861063 + 0.625599i
\(521\) 4.74671 14.6089i 0.207957 0.640026i −0.791622 0.611011i \(-0.790763\pi\)
0.999579 0.0290150i \(-0.00923706\pi\)
\(522\) 0 0
\(523\) 16.0623 11.6699i 0.702356 0.510291i −0.178343 0.983968i \(-0.557074\pi\)
0.880699 + 0.473677i \(0.157074\pi\)
\(524\) −28.7984 −1.25806
\(525\) 0 0
\(526\) −13.6525 −0.595276
\(527\) 1.85410 1.34708i 0.0807660 0.0586799i
\(528\) 0 0
\(529\) 13.8541 42.6385i 0.602352 1.85385i
\(530\) −2.33688 + 7.19218i −0.101508 + 0.312408i
\(531\) 0 0
\(532\) −15.3262 −0.664477
\(533\) −7.85410 24.1724i −0.340199 1.04702i
\(534\) 0 0
\(535\) −18.8435 13.6906i −0.814674 0.591895i
\(536\) −16.7082 + 12.1392i −0.721684 + 0.524334i
\(537\) 0 0
\(538\) 8.61803 + 6.26137i 0.371550 + 0.269947i
\(539\) 2.70820 1.96763i 0.116651 0.0847516i
\(540\) 0 0
\(541\) 10.6180 + 7.71445i 0.456505 + 0.331670i 0.792159 0.610315i \(-0.208957\pi\)
−0.335654 + 0.941985i \(0.608957\pi\)
\(542\) 1.52786 + 4.70228i 0.0656274 + 0.201980i
\(543\) 0 0
\(544\) −1.32624 4.08174i −0.0568620 0.175003i
\(545\) −6.90983 21.2663i −0.295985 0.910947i
\(546\) 0 0
\(547\) −10.7254 + 33.0095i −0.458586 + 1.41138i 0.408287 + 0.912854i \(0.366126\pi\)
−0.866873 + 0.498529i \(0.833874\pi\)
\(548\) −7.78115 + 5.65334i −0.332394 + 0.241499i
\(549\) 0 0
\(550\) −2.36068 −0.100660
\(551\) −8.09017 −0.344653
\(552\) 0 0
\(553\) −1.54508 + 4.75528i −0.0657037 + 0.202215i
\(554\) 2.15654 6.63715i 0.0916227 0.281986i
\(555\) 0 0
\(556\) −2.50000 7.69421i −0.106024 0.326307i
\(557\) −9.23607 −0.391345 −0.195672 0.980669i \(-0.562689\pi\)
−0.195672 + 0.980669i \(0.562689\pi\)
\(558\) 0 0
\(559\) 7.28115 + 5.29007i 0.307960 + 0.223746i
\(560\) 2.07295 + 6.37988i 0.0875981 + 0.269599i
\(561\) 0 0
\(562\) 0.545085 + 0.396027i 0.0229930 + 0.0167054i
\(563\) 7.78115 + 5.65334i 0.327936 + 0.238260i 0.739555 0.673097i \(-0.235036\pi\)
−0.411618 + 0.911356i \(0.635036\pi\)
\(564\) 0 0
\(565\) 7.01064 + 21.5765i 0.294940 + 0.907732i
\(566\) −11.5729 8.40824i −0.486447 0.353425i
\(567\) 0 0
\(568\) 9.79837 0.411131
\(569\) −9.10739 28.0297i −0.381802 1.17506i −0.938774 0.344534i \(-0.888037\pi\)
0.556972 0.830531i \(-0.311963\pi\)
\(570\) 0 0
\(571\) 9.92705 30.5523i 0.415434 1.27857i −0.496428 0.868078i \(-0.665355\pi\)
0.911862 0.410497i \(-0.134645\pi\)
\(572\) 1.85410 5.70634i 0.0775239 0.238594i
\(573\) 0 0
\(574\) 5.23607 0.218549
\(575\) 33.3156 + 24.2052i 1.38936 + 1.00943i
\(576\) 0 0
\(577\) −30.5623 + 22.2048i −1.27233 + 0.924399i −0.999293 0.0376062i \(-0.988027\pi\)
−0.273033 + 0.962005i \(0.588027\pi\)
\(578\) 3.13525 9.64932i 0.130409 0.401359i
\(579\) 0 0
\(580\) 1.54508 + 4.75528i 0.0641562 + 0.197452i
\(581\) −0.881966 2.71441i −0.0365901 0.112613i
\(582\) 0 0
\(583\) −1.29180 3.97574i −0.0535007 0.164658i
\(584\) 16.2812 + 11.8290i 0.673719 + 0.489485i
\(585\) 0 0
\(586\) 14.2361 10.3431i 0.588087 0.427270i
\(587\) 15.1353 + 10.9964i 0.624699 + 0.453870i 0.854560 0.519353i \(-0.173827\pi\)
−0.229861 + 0.973224i \(0.573827\pi\)
\(588\) 0 0
\(589\) −14.2082 + 10.3229i −0.585439 + 0.425346i
\(590\) −4.63525 3.36771i −0.190830 0.138646i
\(591\) 0 0
\(592\) 2.42705 + 7.46969i 0.0997512 + 0.307003i
\(593\) 22.0902 0.907135 0.453567 0.891222i \(-0.350151\pi\)
0.453567 + 0.891222i \(0.350151\pi\)
\(594\) 0 0
\(595\) 0.854102 2.62866i 0.0350148 0.107764i
\(596\) 6.97214 21.4580i 0.285590 0.878955i
\(597\) 0 0
\(598\) 19.9894 14.5231i 0.817426 0.593894i
\(599\) 0.527864 0.0215679 0.0107840 0.999942i \(-0.496567\pi\)
0.0107840 + 0.999942i \(0.496567\pi\)
\(600\) 0 0
\(601\) 36.2705 1.47950 0.739752 0.672879i \(-0.234943\pi\)
0.739752 + 0.672879i \(0.234943\pi\)
\(602\) −1.50000 + 1.08981i −0.0611354 + 0.0444175i
\(603\) 0 0
\(604\) 2.78115 8.55951i 0.113164 0.348281i
\(605\) −18.8435 + 13.6906i −0.766096 + 0.556601i
\(606\) 0 0
\(607\) −15.4377 −0.626597 −0.313298 0.949655i \(-0.601434\pi\)
−0.313298 + 0.949655i \(0.601434\pi\)
\(608\) 10.1631 + 31.2789i 0.412169 + 1.26853i
\(609\) 0 0
\(610\) 5.26393 3.82447i 0.213130 0.154848i
\(611\) 6.35410 4.61653i 0.257059 0.186765i
\(612\) 0 0
\(613\) −25.8713 18.7966i −1.04493 0.759188i −0.0736905 0.997281i \(-0.523478\pi\)
−0.971242 + 0.238093i \(0.923478\pi\)
\(614\) 2.38197 1.73060i 0.0961283 0.0698413i
\(615\) 0 0
\(616\) 2.23607 + 1.62460i 0.0900937 + 0.0654569i
\(617\) −3.01722 9.28605i −0.121469 0.373842i 0.871772 0.489911i \(-0.162971\pi\)
−0.993241 + 0.116069i \(0.962971\pi\)
\(618\) 0 0
\(619\) 12.1976 + 37.5402i 0.490261 + 1.50887i 0.824213 + 0.566279i \(0.191618\pi\)
−0.333952 + 0.942590i \(0.608382\pi\)
\(620\) 8.78115 + 6.37988i 0.352660 + 0.256222i
\(621\) 0 0
\(622\) −5.63525 + 17.3435i −0.225953 + 0.695412i
\(623\) −11.7082 + 8.50651i −0.469079 + 0.340806i
\(624\) 0 0
\(625\) −20.2254 + 14.6946i −0.809017 + 0.587785i
\(626\) 13.1246 0.524565
\(627\) 0 0
\(628\) 4.59017 14.1271i 0.183168 0.563732i
\(629\) 1.00000 3.07768i 0.0398726 0.122715i
\(630\) 0 0
\(631\) −1.78115 5.48183i −0.0709066 0.218228i 0.909323 0.416090i \(-0.136600\pi\)
−0.980230 + 0.197862i \(0.936600\pi\)
\(632\) 6.90983 0.274858
\(633\) 0 0
\(634\) 11.8262 + 8.59226i 0.469680 + 0.341242i
\(635\) 35.5279 1.40988
\(636\) 0 0
\(637\) −17.2082 12.5025i −0.681814 0.495367i
\(638\) 0.527864 + 0.383516i 0.0208983 + 0.0151835i
\(639\) 0 0
\(640\) 20.5902 14.9596i 0.813898 0.591331i
\(641\) 8.16312 + 5.93085i 0.322424 + 0.234255i 0.737209 0.675665i \(-0.236143\pi\)
−0.414785 + 0.909919i \(0.636143\pi\)
\(642\) 0 0
\(643\) 22.8328 0.900438 0.450219 0.892918i \(-0.351346\pi\)
0.450219 + 0.892918i \(0.351346\pi\)
\(644\) −6.66312 20.5070i −0.262564 0.808088i
\(645\) 0 0
\(646\) 0.854102 2.62866i 0.0336042 0.103423i
\(647\) −9.43769 + 29.0462i −0.371034 + 1.14193i 0.575082 + 0.818096i \(0.304970\pi\)
−0.946116 + 0.323829i \(0.895030\pi\)
\(648\) 0 0
\(649\) 3.16718 0.124323
\(650\) 4.63525 + 14.2658i 0.181810 + 0.559553i
\(651\) 0 0
\(652\) 14.3992 10.4616i 0.563916 0.409709i
\(653\) −2.44427 + 7.52270i −0.0956518 + 0.294386i −0.987423 0.158101i \(-0.949463\pi\)
0.891771 + 0.452487i \(0.149463\pi\)
\(654\) 0 0
\(655\) −12.2984 + 37.8505i −0.480537 + 1.47894i
\(656\) 3.00000 + 9.23305i 0.117130 + 0.360490i
\(657\) 0 0
\(658\) 0.500000 + 1.53884i 0.0194920 + 0.0599903i
\(659\) 19.7984 + 14.3844i 0.771235 + 0.560335i 0.902336 0.431034i \(-0.141851\pi\)
−0.131101 + 0.991369i \(0.541851\pi\)
\(660\) 0 0
\(661\) 32.9164 23.9152i 1.28030 0.930192i 0.280738 0.959784i \(-0.409421\pi\)
0.999562 + 0.0295922i \(0.00942086\pi\)
\(662\) 8.56231 + 6.22088i 0.332783 + 0.241781i
\(663\) 0 0
\(664\) −3.19098 + 2.31838i −0.123834 + 0.0899708i
\(665\) −6.54508 + 20.1437i −0.253808 + 0.781139i
\(666\) 0 0
\(667\) −3.51722 10.8249i −0.136187 0.419142i
\(668\) −9.00000 −0.348220
\(669\) 0 0
\(670\) 3.94427 + 12.1392i 0.152381 + 0.468979i
\(671\) −1.11146 + 3.42071i −0.0429073 + 0.132055i
\(672\) 0 0
\(673\) 8.23607 5.98385i 0.317477 0.230661i −0.417621 0.908621i \(-0.637136\pi\)
0.735098 + 0.677961i \(0.237136\pi\)
\(674\) −0.708204 −0.0272790
\(675\) 0 0
\(676\) −17.0902 −0.657314
\(677\) 6.78115 4.92680i 0.260621 0.189352i −0.449800 0.893129i \(-0.648505\pi\)
0.710421 + 0.703777i \(0.248505\pi\)
\(678\) 0 0
\(679\) −1.42705 + 4.39201i −0.0547652 + 0.168550i
\(680\) −3.81966 −0.146477
\(681\) 0 0
\(682\) 1.41641 0.0542371
\(683\) 1.39919 + 4.30625i 0.0535384 + 0.164774i 0.974251 0.225468i \(-0.0723912\pi\)
−0.920712 + 0.390242i \(0.872391\pi\)
\(684\) 0 0
\(685\) 4.10739 + 12.6412i 0.156935 + 0.482997i
\(686\) 9.20820 6.69015i 0.351571 0.255431i
\(687\) 0 0
\(688\) −2.78115 2.02063i −0.106030 0.0770356i
\(689\) −21.4894 + 15.6129i −0.818679 + 0.594805i
\(690\) 0 0
\(691\) −2.20820 1.60435i −0.0840040 0.0610325i 0.544991 0.838442i \(-0.316533\pi\)
−0.628995 + 0.777410i \(0.716533\pi\)
\(692\) −8.44427 25.9888i −0.321003 0.987946i
\(693\) 0 0
\(694\) −5.93769 18.2743i −0.225392 0.693685i
\(695\) −11.1803 −0.424094
\(696\) 0 0
\(697\) 1.23607 3.80423i 0.0468194 0.144095i
\(698\) 4.14590 3.01217i 0.156925 0.114012i
\(699\) 0 0
\(700\) 13.0902 0.494762
\(701\) −35.0132 −1.32243 −0.661214 0.750197i \(-0.729959\pi\)
−0.661214 + 0.750197i \(0.729959\pi\)
\(702\) 0 0
\(703\) −7.66312 + 23.5847i −0.289020 + 0.889512i
\(704\) −0.0557281 + 0.171513i −0.00210033 + 0.00646416i
\(705\) 0 0
\(706\) 4.60081 + 14.1598i 0.173154 + 0.532913i
\(707\) −12.0902 −0.454698
\(708\) 0 0
\(709\) −27.1353 19.7149i −1.01909 0.740409i −0.0529906 0.998595i \(-0.516875\pi\)
−0.966095 + 0.258186i \(0.916875\pi\)
\(710\) 1.87132 5.75934i 0.0702295 0.216144i
\(711\) 0 0
\(712\) 16.1803 + 11.7557i 0.606384 + 0.440564i
\(713\) −19.9894 14.5231i −0.748607 0.543895i
\(714\) 0 0
\(715\) −6.70820 4.87380i −0.250873 0.182270i
\(716\) 12.3992 + 9.00854i 0.463379 + 0.336665i
\(717\) 0 0
\(718\) −17.7639 −0.662944
\(719\) 11.3435 + 34.9116i 0.423040 + 1.30198i 0.904859 + 0.425712i \(0.139976\pi\)
−0.481819 + 0.876271i \(0.660024\pi\)
\(720\) 0 0
\(721\) 5.78115 17.7926i 0.215301 0.662630i
\(722\) −2.91641 + 8.97578i −0.108537 + 0.334044i
\(723\) 0 0
\(724\) −22.1803 −0.824326
\(725\) 6.90983 0.256625
\(726\) 0 0
\(727\) −3.59017 + 2.60841i −0.133152 + 0.0967406i −0.652368 0.757903i \(-0.726224\pi\)
0.519216 + 0.854643i \(0.326224\pi\)
\(728\) 5.42705 16.7027i 0.201140 0.619045i
\(729\) 0 0
\(730\) 10.0623 7.31069i 0.372423 0.270581i
\(731\) 0.437694 + 1.34708i 0.0161887 + 0.0498237i
\(732\) 0 0
\(733\) 8.33688 + 25.6583i 0.307930 + 0.947710i 0.978568 + 0.205925i \(0.0660204\pi\)
−0.670638 + 0.741785i \(0.733980\pi\)
\(734\) −2.71885 1.97536i −0.100354 0.0729118i
\(735\) 0 0
\(736\) −37.4336 + 27.1971i −1.37982 + 1.00250i
\(737\) −5.70820 4.14725i −0.210264 0.152766i
\(738\) 0 0
\(739\) 25.0623 18.2088i 0.921932 0.669823i −0.0220723 0.999756i \(-0.507026\pi\)
0.944004 + 0.329934i \(0.107026\pi\)
\(740\) 15.3262 0.563404
\(741\) 0 0
\(742\) −1.69098 5.20431i −0.0620779 0.191056i
\(743\) 16.3607 0.600215 0.300108 0.953905i \(-0.402977\pi\)
0.300108 + 0.953905i \(0.402977\pi\)
\(744\) 0 0
\(745\) −25.2254 18.3273i −0.924188 0.671462i
\(746\) −1.00658 + 3.09793i −0.0368534 + 0.113423i
\(747\) 0 0
\(748\) 0.763932 0.555029i 0.0279321 0.0202939i
\(749\) 16.8541 0.615835
\(750\) 0 0
\(751\) −40.8885 −1.49204 −0.746022 0.665921i \(-0.768039\pi\)
−0.746022 + 0.665921i \(0.768039\pi\)
\(752\) −2.42705 + 1.76336i −0.0885054 + 0.0643030i
\(753\) 0 0
\(754\) 1.28115 3.94298i 0.0466568 0.143595i
\(755\) −10.0623 7.31069i −0.366205 0.266063i
\(756\) 0 0
\(757\) 3.58359 0.130248 0.0651239 0.997877i \(-0.479256\pi\)
0.0651239 + 0.997877i \(0.479256\pi\)
\(758\) 6.60739 + 20.3355i 0.239991 + 0.738617i
\(759\) 0 0
\(760\) 29.2705 1.06175
\(761\) 30.2984 22.0131i 1.09832 0.797973i 0.117531 0.993069i \(-0.462502\pi\)
0.980784 + 0.195096i \(0.0625020\pi\)
\(762\) 0 0
\(763\) 13.0902 + 9.51057i 0.473896 + 0.344306i
\(764\) 31.6525 22.9969i 1.14515 0.831998i
\(765\) 0 0
\(766\) 5.68034 + 4.12701i 0.205239 + 0.149115i
\(767\) −6.21885 19.1396i −0.224550 0.691092i
\(768\) 0 0
\(769\) −4.14590 12.7598i −0.149505 0.460129i 0.848058 0.529904i \(-0.177772\pi\)
−0.997563 + 0.0697749i \(0.977772\pi\)
\(770\) 1.38197 1.00406i 0.0498026 0.0361837i
\(771\) 0 0
\(772\) 2.85410 8.78402i 0.102721 0.316144i
\(773\) 26.8262 19.4904i 0.964873 0.701021i 0.0105954 0.999944i \(-0.496627\pi\)
0.954277 + 0.298923i \(0.0966273\pi\)
\(774\) 0 0
\(775\) 12.1353 8.81678i 0.435911 0.316708i
\(776\) 6.38197 0.229099
\(777\) 0 0
\(778\) 2.86475 8.81678i 0.102706 0.316097i
\(779\) −9.47214 + 29.1522i −0.339374 + 1.04449i
\(780\) 0 0
\(781\) 1.03444 + 3.18368i 0